Let z = cos θ + i sin... |JEE Advanced 2009| Complex Numbers

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JEE Advance 2009

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Question

Let $\mathrm{z}=\cos \theta+\mathrm{i} \sin \theta$. Then the value of $\sum_{\mathrm{m}=1}^{15} \operatorname{Im}\left(\mathrm{z}^{2 \mathrm{~m}-1}\right)$ at $\theta=2^{\circ}$ is

Select the correct option:

A

$\frac{1}{\sin 2^{\circ}}$

B

$\frac{1}{3 \sin 2^{\circ}}$

C

$\frac{1}{2 \sin 2^{\circ}}$

D

$\frac{1}{4 \sin 2^{\circ}}$

✓ Correct! Well done.

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